Internal-wave interactions in the induced-diffusion approximation
- 20 April 1982
- journal article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 117, 315-341
- https://doi.org/10.1017/s0022112082001657
Abstract
Dynamical equations for the interaction of high-wavenumber, high-frequency internal waves with a prescribed, linear, large-scale internal-wave field are obtained from the Boussinesq–Euler equations. The relationship of these ‘induced-diffusion’ interactions to the Taylor–Goldstein equation is discussed. Exact equations are derived in the induced-diffusion limit of McComas & Bretherton (1977) for the evolution of the first and second moments of the small-scale flow when the large-scale flow is assumed random. Estimates of corrections to the induced-diffusion approximation for the Garrett–Munk internal-wave model indicate the domain of applicability of these equations. Computations of the autocorrelation function and action transport in wavenumber and physical space are presented. Severe limitations are found on the applicability of two-time perturbation theory and the resonant-interaction approximation. The high transfer rates found by McComas & Bretherton in the induceddiffusion regime are reduced significantly in the present calculations.Keywords
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